Abstract
We introduce decision P systems,which are a class of P systems with symbol-objects and external output. The main result of the paper is the following:if there exists an NP-complete problem that cannot be solved in polynomial time,with respect to the input length,by a deterministic decision P system constructed in polynomial time,then P≠NP. From Zandron-Ferreti-Mauri’s theorem it follows that if P≠ NP,then no NP-complete problem can be solved in polynomial time, with respect to the input length,by a deterministic P system with active membranes but without membrane division,constructed in polynomial time from the input. Together,these results give a characterization of P≠NP in terms of deterministic P systems.
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Pérez Jiménez, M.J., Romero Jiménez, Á., Sancho Caparrini, F. (2003). Decision P Systems and the P≠NP Conjecture. In: PĂun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. WMC 2002. Lecture Notes in Computer Science, vol 2597. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36490-0_27
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DOI: https://doi.org/10.1007/3-540-36490-0_27
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